so first of all, I just want to point out that I am a beginner, so cut me some slack.
As the title says I have 3 circles.
I know the coordinates of each center and the radius of each circle.
What I want to know is a formula that I can calculate the intersection point(points) with if any are present.
As the picture:
3 circles
Thank you for your help!!
Best Answer
Generally you can represent circles with a center $(x_0,y_0)$ and a radius $r$ in the following form, using the pythagorean theorem: The points $(x,y)$ on this circle are exactly the points that satisfy
$$(x-x_0)^2 + (y-y_0)^2 = r^2$$
You can write down this equation for all three circles. By evaluating the difference between each pair of equations (note that $x^2$ and $y^2$ will cancel out), you get three lines that go throu the two intersection points of the corresponding pair of circles. Now you can just find the intersection of those lines.